Question 308829: Two sides of a triangle measure 2x – 4 and 7x – 2 units, respectively. Which of these is a possible length for the third side of the triangle?
A)
3x units
B)
6x units
C)
5x + 2 units
D)
9x – 6 units
Found 3 solutions by user_dude2008, stanbon, solver91311:
Answer by user_dude2008(1862)   (Show Source):
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Two sides of a triangle measure 2x – 4 and 7x – 2 units, respectively. Which of these is a possible length for the third side of the triangle?
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Let the 3rd side meansure M
M< (2x-4)+(7x-2) = 9x-6
M> (7x-2)-(2x-4) = 5x+2
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5x+2 < M < 9x-6
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A)
3x units
Not in the interval
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B)
6x units
In the interval.
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C)
5x + 2 units
Not in the interval.
D)
9x – 6 units
Not in the interval
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Cheers,
Stan H.
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
Given that  is allowed to be any real number, any of the answers A), B), and C) could work. But answer D) is the sum of the measures of the other two sides, and in order to have a triangle the measure of any third side must be strictly less than the sum of the other two sides (this is called the triangle inequality).
So, as worded, the correct answer is A), B), or C)
John
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